Hi guys. You know that a vector space V is a set with two operations + and * that satisfy the following properties. However last statement seems to be too obvious (1*u = u) so: Is there a space which satisfies with the first 9 statements and it doesn't satifies the last one (1 * u = u). Thanks or your help!

I can't think of anything. To be honest, when I was taking matrix algebra and was testing vector spaces, my first tests would be the zero properties and the 1 properties, because those were where things would "pass" or "fail".